[hist-analytic] Elizabeth Anscombe's Intention (New "Look Inside" feature)
Roger Bishop Jones
rbj at rbjones.com
Wed Jun 16 15:51:09 EDT 2010
On Wednesday 16 Jun 2010 17:27, you wrote:
> Amazon has introduced the "Look Inside" feature of my
> book _Elizabeth Anscombe's Intention_.
Looks good!
> One thing on my mind as I do some
> math needed for economics is the idea of a Limit in
> calculus. You can simply substitute 'a' for 'x' in Lim
> f(x) when f(a) is defined;
> x->a
>
> That is,
>
> Lim f(x) = fa
> x -> a
This is a definition of continuity, it won't hold, even if
f(a) is defined, if there is a discontinuty at a.
Also, there may not be a limit either,
Lim f(x)
x -> a
does not always exist.
> But it is defined when x goes to a, where *a* is never
> reached.
The limit may then be defined, but won't necessarily = f(a)
and definitely won't, of course, if f is not defined at a.
> So the limit may be defined even when 'a'
> doesn't exist (as what x goes to), or so it seems.
I presume you mean here f is not defined at a, rather than
that a does not exist.
> My concern here is that quantification, e.g. UG, may be
> possible where a does not exist.
This doesn't happen in any logic I know of, i.e. you only
quantify over things which do exist.
(I dare say if you were keen you could formalise a
Meinongian logic in which unusual things happen.)
However, you can write something like:
for all x such that P x then Q x.
which is a way of quantifying over P's whether or not there
are any.
In that case you might say, if P is always false, that you
have quantified over something which does not exist, though I
think that's a confusing way of putting it. Really you did
a restricted quantification the effect of which was to
quantify over nothing.
Roger Jones
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